### Recursion

In C, it is possible for the functions to call themselves. A function is called ‘recursive’ if a statement within the body of a function calls the same function. Sometimes called ‘circular definition’, recursion is thus the process of defining something in terms of itself.

Let us now see a simple example of recursion. Suppose we want to calculate the factorial value of an integer. As we know, the factorial of a number is the product of all the integers between 1 and that number. For example, 4 factorial is 4 * 3 * 2 * 1. This can also be expressed as 4! = 4 * 3! where ‘!’ stands for factorial. Thus factorial of a number can be expressed in the form of itself. Hence this can be programmed using recursion. However, before we try to write a recursive function for calculating factorial let us take a look at the non-recursive function for calculating the factorial value of an integer.

```#include<stdio.h>
int main( )
{
int a, fact ;
printf ( "\nEnter any number " ) ;
scanf ( "%d", &a ) ;
fact = factorial ( a ) ;
printf ( "Factorial value = %d", fact ) ;
}

int factorial ( int x )
{
int f = 1, i ;
for ( i = x ; i >= 1 ; i-- )
f = f * i ;

return ( f ) ;
}
```

Work through the above program carefully, till you understand the logic of the program properly. Recursive factorial function can be understood only if you are thorough with the above logic.

Following is the recursive version of the function to calculate the factorial value.

```#include<stdio.h>
int main( )
{
int a, fact ;
printf ( "\nEnter any number " ) ;
scanf ( "%d", &a ) ;
fact = rec ( a ) ;
printf ( "Factorial value = %d", fact ) ;
}
int rec ( int x )
{
int f ;
if ( x == 1 )
return ( 1 ) ;
else
f = x * rec ( x - 1 ) ; // recusrsive call

return ( f ) ;
}
```

Let us understand this recursive factorial function thoroughly. In the first run when the number entered through scanf( ) is 1, let us see what action does rec( ) take. The value of a (i.e. 1) is copied into x. Since x turns out to be 1 the condition if ( x == 1 ) is satisfied and hence 1 (which indeed is the value of 1 factorial) is returned through the return statement.
When the number entered through scanf( ) is 2, the ( x == 1 ) test fails, so we reach the statement,

```f = x * rec ( x - 1 ) ;
```

And here is where we meet recursion. How do we handle the expression x * rec ( x – 1 )? We multiply x by rec ( x – 1 ). Since the current value of x is 2, it is same as saying that we must calculate the value (2 * rec ( 1 )). We know that the value returned by rec ( 1 ) is 1, so the expression reduces to (2 * 1), or simply 2. Thus the statement,

```x * rec ( x - 1 ) ;
```

evaluates to 2, which is stored in the variable f, and is returned to main( ), where it is duly printed as :

Factorial value = 2

Now perhaps you can see what would happen if the value of a is 3, 4, 5 and so on.

In case the value of a is 5, main( ) would call rec( ) with 5 as its actual argument, and rec( ) will send back the computed value. But before sending the computed value, rec( ) calls rec( ) and waits for a value to be returned. It is possible for the rec( ) that has just been called to call yet another rec( ), the argument x being decreased in value by 1 for each of these recursive calls. We speak of this series of calls to rec( ) as being different invocations of rec( ). These successive invocations of the same function are possible because the C compiler keeps track of which invocation calls which. These recursive invocations end finally when the last invocation gets an argument value of 1, which the preceding invocation of rec( ) now uses to calculate its own f value and so on up the ladder. So we might say what happens is,

rec ( 5 ) returns ( 5 times rec ( 4 ),
which returns ( 4 times rec ( 3 ),
which returns ( 3 times rec ( 2 ),
which returns ( 2 times rec ( 1 ),
which returns ( 1 ) ) ) ) )